Boundedness and compactness of operators between different spaces are the important component part in operator fields, so many researchers of operator theory have a profound and systematic study on this field. In fact, because people can discuss a lot of space, the operator is not unique, so research in this area has been continually updated. This paper was inspired from reference[1 -2]. In addition, learn the definition of Dirichlet space from reference[3]. The boundness and compactness of operator Lg: D2→Zμ were discussed, the conclusion was clarity and it was easy to understand. Moreover, difference operator Lg～Lh :D2→Zμ could also be discussed by the same way, but due to space constraints, not shown in this paper.%空间之间算子的有界性及紧性是算子理论的重要组成部分,因此诸多算子理论方向的研究人员对这个问题进行了深刻而系统的讨论.事实上,由于可以讨论的空间很多,算子也不惟一,所以这方面的研究成果一直在不断更新中.基于文献[1-2]中对Zygmund空间及Bloch空间之间积分算子的讨论,并且借鉴了文献[3]中单位球上Dirichlet空间的定义及空间中的函数估计式.给出了单位球上算子Lg:D2→Zμ有界性及紧性的充要条件,结论清晰明了,很容易理解.此外按照同样的方法可以讨论差分Lg-Lh:D2→Zμ有界性及紧性的充要条件,但由于篇幅限制未做出介绍.
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